Unlike a photon resonance between particles, which is a one dimensional D-brane string with Dirichlet boundary conditions, a particle spin has cyclic boundary conditions and so is a 0-brane loop string and not a D-brane string. Since particle spin dimensions do not map directly into 3D space and time, for quantum energy calculations, typically two dimensional Dirac spinors represent spin dimensions separately from 3D space and time. Given that spin resonance energies tend to be much smaller than other quantum orbit resonances, this spin-orbit separation of variables works very well for many energy calculations that include average spin.
When instantaneous quantum phase matching is important, though, the 0-brane loop string is then useful since it shows both mass and charge oscillation as a 0-brane loops as well as the three D-brane magnetic fibers that take a 4𝜋 rotation to return spin magnetic identity. The figure below shows how the spin D-brane fibers do not cross each other and therefore maintain their orthogonality.
Since quantum phase matching is still an issue with the resonance of spin-orbit coupling, the 0-brane spin phase is useful for matching the D-brane orbital phase. In the first excited state of hydrogen, the coupling of the electron spin magnetism to the electron orbit magnetism results in the fine structure of the hydrogen spectrum. The figure shows three of the many different short-lived electron P-type orbital resonances. There is only a well-defined average electron energy and radius for the hydrogen fine structure.
